Unable to install or uninstall any apps

If you have an apt-get dependency problem after the update, it seems the app installer won't proceed with some installs. It's not surprising because you wouldn't not want to force an update which is not consistent. For plex if you installed vim on an earlier version that seems to be the cause because it has a dependency which doesn't automatically resolve. I say seems to be because I did encounter this but it still took some random effort to get past the problem and I don't konw what finally cleared it. See https://community.netgear.com/t5/Using-your-ReadyNAS/Plex-Broken-after-upgrade-to-6-7-3/m-p/1290476#M130617.

More generally, when an install fails, if you can find the apps .deb file (sometimes left behind in /tmp), then from ssh you can try to install it using dpkg/apt-get. Apt-get will tell you about the dependency problem. Fix that then go back to the web and try the install again. If you never used ssh, then probably work with netgear support instead :-).